1 Chapter 5 LL (1) Grammars and Parsers

2 Naming of parsing techniques The way to parse token sequence L: Leftmost R: Righmost Top-down  LL Bottom-up  LR

3 The LL(1) Predict Function Given the productions A  1 A  2 … A  n During a (leftmost) derivation … A …  …  1 …or …  2 …or …  n … Deciding which production to match –Using lookahead symbols

4 The LL(1) Predict Function The limitation of LL(1) –LL(1) contains exactly those grammars that have disjoint predict sets for productions that share a common left-hand side Single Symbol Lookahead

5 Not extended BNF form $: end of file token

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8 The LL(1) Parse Table The parsing information contain in the Predict function can be conveniently represented in an LL(1) parse table T:V n x V t  P  {Error} where P is the set of all productions The definition of T T[A][t]= A  X 1  X m if t  Predict( A  X 1  X m ); T[A][t]=Error otherwise

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10 The LL(1) Parse Table A grammar G is LL(1) if and only if all entries in T contain a unique prediction or an error flag

11 Building Recursive Descent Parsers from LL(1) Tables Similar the implementation of a scanner, there are two kinds of parsers –Build in The parsing decisions recorded in LL(1) tables can be hardwired into the parsing procedures used by recursive descent parsers –Table-driven

12 Building Recursive Descent Parsers from LL(1) Tables The form of parsing procedure: The name of the nonterminal the parsing procedure handles A sequence of parsing actions

13 Building Recursive Descent Parsers from LL(1) Tables E.g. of an parsing procedure for in Micro

14 Building Recursive Descent Parsers from LL(1) Tables An algorithm that automatically creates parsing procedures like the one in Figure 5.6 from LL(1) table

15 Building Recursive Descent Parsers from LL(1) Tables The data structure for describing grammars Name of the symbols in grammar

16 Building Recursive Descent Parsers from LL(1) Tables gen_actions() –Takes the grammar symbols and generates the actions necessary to match them in a recursive descent parse

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18 An LL(1) Parser Driver Rather than using the LL(1) table to build parsing procedures, it is possible to use the table in conjunction with a driver program to form an LL(1) parser Smaller and faster than a corresponding recursive descent parser Changing a grammar and building a new parser is easy –New LL(1) table are computed and substituted for the old tables

19 A  aBcD A D c B a

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21 LL(1) Action Symbols During parsing, the appearance of an action symbol in a production will serve to initiate the corresponding semantic action – a call to the corresponding semantic routine. gen_action(“ID:= #gen_assign;”) match(ID); match(ASSIGN); expression(); gen_assign(); match(semicolon); What are action symbols? (See next page.)

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23 LL(1) Action Symbols The semantic routine calls pass no explicit parameters –Necessary parameters are transmitted through a semantic stack –semantic stack  parse stack Semantic stack is a stack of semantic records. Action symbols are pushed to the parse stack –See figure 5.11

24 Difference between Fig. 5.9 and Fig 5.11

25 Making Grammars LL(1) Not all grammars are LL(1). However, some non-LL(1) grammars can be made LL(1) by simple modifications. When a grammar is not LL(1) ? This is called a conflict, which means we do not know which production to use when is on stack top and ID is the next input token. ID 2,3

26 Making Grammars LL(1) Major LL(1) prediction conflicts –Common prefixes –Left recursion Common prefixes  if then end if;  if then else end if; Solution: factoring transform –See figure 5.12

27 Making Grammars LL(1)  if then  end if;  else end if;

28 Making Grammars LL(1) Grammars with left-recursive production can never be LL(1) A  A  –Why? A will be the top stack symbol, and hence the same production would be predicted forever

29 Making Grammars LL(1) Solution: Figure 5.13 AAA…AAAA…A A  NT N  … N  T  T 

30 Making Grammars LL(1) Other transformation may be needed –No common prefixes, no left recursion 1  2  ID : 3  4  ID := ; ID 2,3

31 Making Grammars LL(1) Lookahead two tokens seems be needed! LL(2) ? Example A:B := C ; B := C ;

32 Making Grammars LL(1)  ID  :  := ;  ID := ; Solution: An equivalent LL(1) grammar ! Example A:B := C ; B := C ;

33 Making Grammars LL(1) In Ada, we may declare arrays as A: array(I.. J, BOOLEAN) A straightforward grammar for array bound ..  ID Solution  .. 

34 Making Grammars LL(1) Greibach Normal Form –Every production is of the form A  a  “a” is a terminal and  is (possible empty) string of variables –Every context-free language L without can be generated by a grammar in Greibach Normal Form –Factoring of common prefixes is easy Given a grammar G, we can –G  GNF  No common prefixes, no left recursion (but may be still not LL(1))

35 The If-Then-Else Problem in LL(1) Parsing “Dangling else” problem in Algo60, Pascal, and C –else clause is optional BL={[ i ] j | i  j  0} [  if then ]  else BL is not LL(1) and in fact not LL(k) for any k

36 The If-Then-Else Problem in LL(1) First try –G 1 : S  [ S CL S  CL  ] CL  G 1 is ambiguous: E.g., [[] S [ S CL ] S [ S CL ] Why an ambiguous grammar is not LL(1)? Please try to answer this question according to this figure.

37 Second try –G 2 : S  [S S  S1 S1  [S1] S1  G 2 is not ambiguous: E.g., [[] The problem is [  First([S) and [  First(S1) [[  First 2 ([S) and [[  First 2 (S1) –G 2 is not LL(1), nor is it LL(k) for any k. The If-Then-Else Problem in LL(1) [ S1 [ S1 ] S

38 Solution: conflicts + special rules –G 3 : G  S; S  if S E S  Other E  else S E  G 3 is ambiguous We can enforce that T[E, else] = 4th rule. This essentially forces “else “ to be matched with the nearest unpaired “ if “. The If-Then-Else Problem in LL(1)

39 If all if statements are terminated with an end if, or some equivalent symbol, the problem disappears. S  if S E S  Other E  else S end if E  end if An alternative solution –Change the language The If-Then-Else Problem in LL(1)

40 Properties of LL(1) Parsers A correct, leftmost parse is guaranteed All grammars in the LL(1) class are unambiguous –Some string has two or more distinct leftmost parses –At some point more than one correct prediction is possible All LL(1) parsers operate in linear time and, at most, linear space